Assemble layers of veggies and bubbly cheese a day ahead to save on Turkey Day prep.
Preheat oven to 400°F. Toss together rutabaga, potatoes, parsnips, salt, and 3/4 cup of the cream in a large bowl. Spread one-third of the mixture evenly in a lightly greased 11- x 7-inch baking dish; top with 3/4 cup of the Gruyère. Layer one-third of the rutabaga mixture, 3/4 cup of the Gruyère, and remaining rutabaga mixture and 3/4 cup cream. Top with remaining 1/2 cup Gruyère.
Cover loosely with aluminum foil. Bake in preheated oven 45 minutes. Uncover and bake until vegetables are tender and cheese is golden brown, 20 to 25 minutes. Transfer to a wire rack; cool 5 minutes.